How to select vertices belonging to both faces of two-sided plane?
Turn of Limit Selection to Visible on the 3D View header while in edit mode to select occluded geometry.



You can also select all geometry by default if you switch from shader modes to wireframe mode.

Selection info shows on the Info Editor header, by default above the 3D view, giving you precise scene and selection statistics. It tells how many vertex/edges/faces/objects are in your scene, current object, and how many of those are seletcted

Also if you accidentally/intentionally  move only one at a time, you can then use snapping to perfectly match the first transform by pressing Ctrl while transforming, ensuring a perfect coincidence.